An interesting magnetic physics question about permanent magnets

Main Question or Discussion Point

Imagine for a moment a steel core with no air gap, that is driven to saturation by a powerful permanent magnet. Imagine next that a coil is wrapped around some section of that core some distance away from the magnet, such that their only flux linking is through the saturated core.

The magnet is typical, but powerful enough to saturate the core: it has typical magnet ratings, Hc for its coercivity, Br for is remnant flux. The coil is magic, capable of supporting any amount of current needed for the experiment. The coil is also wrapped very tightly around the core.

What amount of MMF (H) would be put through the coil in order to stop all flux in the core?

One hypothesis is that the current in the coil would need to equal the Hc rating of the magnet in order to stop all flux in the core. My reasoning is that if the coil were to have just a small amount of current, the core would come out of saturation for a moment, allowing the magnet to send yet more flux into the core.

Another hypothesis is that the core is simply a very large reluctance, and the magnet is already producing as much flux as possible given its coercivity. If just a small amount of opposing MMF were generated in opposition to the magnet, all flux should stop.

If I understand your scenario, the opposing magnetic field of the coil would magnetize the core opposite to that of what the permanent magnet is trying to do, though needing to be of a strength greater than that of the permanent magnet.
If not glued to the core, the permanet magnet would fall off, or perhaps fly off.

Still, just my thoughts. I do not have the knowledge to directly answer your questions.